Find the average of each weight interval. For example, if an interval is 4 lbs. to 5 lbs., then the average would be 4.5 lbs.
Multiply the total number of instances in the interval by the average weight of the interval. For example, if there are 23 packages in the 4 lbs. to 5 lbs. interval, then 23 * 4.5 lbs = 103.5 lbs. This number is the estimated total sum of all weights within the interval. It is important to note that this is an estimate, as the average is used in the calculation.
Sum the estimated total sums from each interval to get the total weight of the entire system. For example, if the estimated total sums of a postal service system were 45 lbs. for 0 to 1 lbs., 55 lbs. for 1 to 2 lbs., 65 lbs. for 2 to 3 lbs., 75 lbs. for 3 to 4 lbs. and 103.5 lbs. for 4 to 5 lbs., then the total weight moved by the entire system would be 45 + 55 + 65 + 75 + 103.5, or 343.5 lbs.
Use the data to optimize the system. For example, if there is a noticeably higher number of instances in one weight interval, then increase the price for that interval.